If iCloud Sync stops working or becomes slow, the data in the cloud may have become corrupted and will need to be deleted.
On your computer go to System Preferences... > iCloud/Apple ID > Manage...
From there, select iReal Pro from the list and click on Delete Documents and Data.
This will delete the data in the cloud but not on your device. You can now go back to iReal Pro and enable iCloud Sync again.